Express 5/[(x-1)(3x+2)] as partial fractions.

5 = a(3x+2) + b(x-1), x = 1, 5 = a(3+2) +b (1-1), 5 = a(5) + b(0), 5 = 5a, a = 1, x = -2/3, 5 = a(-2+2) + b(-(2/3)-1), 5 = a(0) + b(-5/3), 5 = -5b/3, b = -3, Therefore: 5/[(x-1)(3x+2)] = 1/(x-1) -3/(3x+2)